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03 Mar 2021, 14:40
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
15%
(low)
Question Stats:
77% (01:01) correct
23%
(00:59)
wrong
based on 112
sessions
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The figure on the left is an isosceles right triangle, and the figure on the right is a square of length 3. Find the value of b.
(1) b is the length of the diagonal of the square.
(2) the triangle and the square have the same area.
Attachment:
triangle1b.jpg [ 4.31 KiB | Viewed 3041 times ]
Pure algebraic questions like this one are no longer part of the GMAT Data Sufficiency syllabus.
For relevant Data Sufficiency questions, please check the Data Sufficiency forum:
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06 Mar 2021, 04:26
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Answer : D - Each statement is sufficient
We know that Square has the side of 3 and the triangle given is an isosceles triangle.
Statement 1 : b = length of the diagonal of the square ------- b = side x √2
b = 3√2 ----- Sufficient
Statement 2 : Area of square = 9 (which is also the area of the triangle )
As the triangle is an isosceles triangle, base and height are equal.
Area of triangle = 1/2 * b * b ------- 9 = 1/2* b^2
b^2 = 18 ------- b = 3√2 ----- Sufficient
Hence D
We know that Square has the side of 3 and the triangle given is an isosceles triangle.
Statement 1 : b = length of the diagonal of the square ------- b = side x √2
b = 3√2 ----- Sufficient
Statement 2 : Area of square = 9 (which is also the area of the triangle )
As the triangle is an isosceles triangle, base and height are equal.
Area of triangle = 1/2 * b * b ------- 9 = 1/2* b^2
b^2 = 18 ------- b = 3√2 ----- Sufficient
Hence D
06 Mar 2021, 12:55
Kudos
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Statement 1: b is the length of the diagonal of the square.
Diagonal of the square = Side * √2 = 3√2 = b (Sufficient)
Statement 2: the triangle and the square have the same area.
Important thing to consider here is that it's an isosceles right triangle.
Hence, base (b) and height (h) of the triangle are same.
Area of triangle = Area of square
1/2*b*h = 3^2
1/2*b*b = 9
b^2 = 18
b = 3√2 (Sufficient)
Answer: D
Diagonal of the square = Side * √2 = 3√2 = b (Sufficient)
Statement 2: the triangle and the square have the same area.
Important thing to consider here is that it's an isosceles right triangle.
Hence, base (b) and height (h) of the triangle are same.
Area of triangle = Area of square
1/2*b*h = 3^2
1/2*b*b = 9
b^2 = 18
b = 3√2 (Sufficient)
Answer: D
